A001463 Partial sums of A001462; also a(n) is the last occurrence of n in A001462. (Formerly M2438 N0965)

1, 3, 5, 8, 11, 15, 19, 23, 28, 33, 38, 44, 50, 56, 62, 69, 76, 83, 90, 98, 106, 114, 122, 131, 140, 149, 158, 167, 177, 187, 197, 207, 217, 228, 239, 250, 261, 272, 284, 296, 308, 320, 332, 344, 357, 370, 383, 396, 409, 422, 436, 450, 464, 478, 492, 506, 521, 536, 551, 566, 581, 596

Offset

1,2

Comments

Vardi gives several identities satisfied by A001463 and this sequence.

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. Marcus and N. J. Fine, Solutions to Problem 5407, Amer. Math. Monthly 74 (1967), 740-743.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

J. L. Rémy, Sur la suite autodécrite de Golomb, J. Number Theory, vol. 66 1997 pp. 1-28.

N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282)

I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 1-11. (See also the Math. Review, 93d:11103)

Formula

a(n) is asymptotic to tau^(1-tau)*n^tau where tau is the golden ratio, tau=(1+sqrt(5))/2. More precisely, a(n)= tau^(1-tau)*n^tau + c*n^(1/tau)+0(n^(1/tau)) where c is a constant around 0.6. Is there any known value for c? - Benoit Cloitre, Oct 29 2002

Mathematica

Accumulate[a[1]=1; a[n_]:=a[n]=1+a[n-a[a[n-1]]]; Table[a[n], {n, 84}]] (* Harvey P. Dale, Oct 20 2011, from Robert G. Wilson v's program in A001463 *)

Prog

(Haskell)
a001463 n = a001463_list !! (n-1)
a001463_list = scanl1 (+) a001462_list
-- Reinhard Zumkeller, Apr 28 2012

Crossrefs

Sequence in context: A108279 A002821 A046992 * A145197 A219656 A024169

Adjacent sequences: A001460 A001461 A001462 * A001464 A001465 A001466

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved